∫{x^2/[(x-3)(x+2)^2]}dx
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∫{x^2/[(x-3)(x+2)^2]}dx
![∫{x^2/[(x-3)(x+2)^2]}dx](/uploads/image/z/665551-55-1.jpg?t=%E2%88%AB%7Bx%5E2%2F%5B%28x-3%29%28x%2B2%29%5E2%5D%7Ddx)
x^2/[(x-3)(x+2)^2=(9/25)[1/(x-3)]+(16/25)[1/(x+2)]-(20/25)[1/(x+2)^2].
原式=(9/25)∫1/(x-3)dx+(16/25)∫1/(x+2)dx-(4/5)∫1/(x+2)^2dx
=(9/25)ln|x-3|+(16/25)ln|x+2|+(4/5)[1/(x+2)]+C.
原式=(9/25)∫1/(x-3)dx+(16/25)∫1/(x+2)dx-(4/5)∫1/(x+2)^2dx
=(9/25)ln|x-3|+(16/25)ln|x+2|+(4/5)[1/(x+2)]+C.